Exploratories

CURVED SPACE LYCRA MODEL

Problem: How do planets move around a star in curved spacetime?

Materials: A square wooden frame at least 2 feet by 2 feet, beige-colored two-way stretch Lycra®, a Sharpie® pen, one heavy spherical object, golfballs or marbles. (Rather than use the frame, students can hold the lycra at the corners during the exploration. Lycra can be purchased at a fabric store. Choose the Lycra that will have the least friction on a rolling ball. Make sure the Lycra stretches in both directions. A piece one yard by two yards is fine).

You can also purchase an orange plastic cone such as are used to block off driveways or parking areas (or lanes on a highway during repairs).

Procedure: The construct grid lines on the materials using a Sharpie pen. Stretch the Lycra® not too tightly on the wooden frame and staple (or have students stretch it). Place the heavy spherical object in the center of the fabric to simulate a star. Note the "curved space lines" created by the heavy object in the middle.

Roll golf balls across the stretched fabric helped and observe the paths of the golf balls.

If you use the plastic cone, cut it to form the four paths that gravity or electricity can give to a particle (mass or charge) moving around the central mass (or charge).

A cut perpendicular to the axis of the cone will give a circle. A cut at an angle to the axis will give an ellipse. A cut parallel to the edge of the cone will give a parabola. A cut parallel to the axis will give a hyperbola.

Summing Up:

1. Do the golf balls move in "straight lines" past the central object? If not, describe their paths.

2. If the heavy object represents a massive star (or charged nucleus) and the Lycra® spacetime (the "fabric of the universe") how would you describe the effect of the star (or charge) on spacetime?

3. Does the "star" affect the planet (golf ball) directly by contact? What is the role of spacetime (Lycra®) in this model?

4. Would spacetime for the entire universe be curved? What would determine whether or not it is curved?

5. Discuss the velocity the ball would need to move in each of the paths described by the cuts of the cone.